How to plot 3D vector data in color with vectors in the same direction grouped as one color?

I have three 3D arrays, P1, P2 and P3. They are the x, y and z components of a vector quantity (polarization). The position of the data in the array represents its position in the space, i.e. P1(1,2,3) indicates the value of x component at coordinate 1,2,3. I would like to view the data as something shown here, Domain Structure. The magnitude does not really matter here, what I would like to achieve is to group the vector quantities that are in the same direction by the same color. May I know what matlab function I can used to achieve this? I have tried quiver3 before, but it is too messy to interpret the plot.

Thank you.